Solve for $x$ and $y$ using elimination. ${-3x+5y = 11}$ ${-5x-4y = -31}$
Answer: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Multiply the top equation by $5$ and the bottom equation by $-3$ ${-15x+25y = 55}$ $15x+12y = 93$ Add the top and bottom equations together. $37y = 148$ $\dfrac{37y}{{37}} = \dfrac{148}{{37}}$ ${y = 4}$ Now that you know ${y = 4}$ , plug it back into $\thinspace {-3x+5y = 11}\thinspace$ to find $x$ ${-3x + 5}{(4)}{= 11}$ $-3x+20 = 11$ $-3x+20{-20} = 11{-20}$ $-3x = -9$ $\dfrac{-3x}{{-3}} = \dfrac{-9}{{-3}}$ ${x = 3}$ You can also plug ${y = 4}$ into $\thinspace {-5x-4y = -31}\thinspace$ and get the same answer for $x$ : ${-5x - 4}{(4)}{= -31}$ ${x = 3}$